Fast clock time coinciding with accurate clock

Question

Clock A gains two minutes every hour. Clock B is accurate. The clocks chime on every quarter hour. Both clocks are set at 12:00 noon on Monday so that they chime together. 

 

a. At what time will they next chime together?

b. At what time and day willo they next chime on the hour together?

Answer 1

it's 12:00 noon on Monday

clock A gains 2 minutes per hour, or 1 minute per 1/2 hour

after 7 hours clock A has gained 14 minutes and it reads 7:14 pm

after 7 hours clock B reads 7:00 pm

after another 1/2 hour goes by clock A has gained 1 minute and reads 7:45 pm (7:14 +31 minutes)

after another 1/2 hour goes by clock B reads 7:30 pm

clock A reads 7:45 pm and chimes and clock B reads 7:00 pm and chimes because they both chime on the quarter hour, therefore they chime together at these different times

 

 

after 30 hours go by clock A has gained 1 hour (31 hours have elapsed for clock A)

12:00 noon on Monday plus 24 hours brings you to 12:00 noon on Tuesday

7 more hours more brings you to 7:00 pm Tuesday for clock A

after 24 hours go by clock B is at 12:00 noon on Tuesday and the after 6 more hours go by clock B is at 6:00 pm on Tuesday

since they are both on the hour, clock A at 7:00 pm and clock B at 6:00 pm, on Tuesday, they will chime together on the hour albeit different hours